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Difficulty: MediumPythagorean Theorem Word Problems

A zip line is being installed from an observation deck down to a ground anchor. The observation deck is 4545 yards directly above the base of the structure. The ground anchor is secured on flat ground 2424 yards horizontally away from the base. Assuming the zip line is pulled perfectly straight, what is the required length of the zip line cable in feet?

  1. A
    51
  2. B
    69
  3. 153Answer
  4. D
    207

Answer

153
The correct answer accurately calculates the diagonal length using the Pythagorean theorem (452+242=c245^2 + 24^2 = c^2, so c=51c = 51 yards) and then converts that distance into feet by multiplying by 3 (51×3=15351 \times 3 = 153 feet).

Step-by-Step Solution

1
Apply the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) to find the diagonal length of the zip line in yards.
242+452=576+2025=260124^2 + 45^2 = 576 + 2025 = 2601 square yards.
The vertical height and horizontal distance form a right triangle with the zip line acting as the hypotenuse.
2
Calculate the square root of the sum to find the actual length.
2601=51\sqrt{2601} = 51 yards.
This isolates cc (the hypotenuse) to give the actual length of the zip line in yards.
3
Convert the length from yards to feet.
51×3=15351 \times 3 = 153 feet.
The question specifically asks for the length in feet, and there are 33 feet in one yard.

Key Concept

Using the Pythagorean theorem to find a hypotenuse and converting units of measurement.
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Topics

Pythagorean Theorem Word Problems

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